Quantum Walks in Two-Dimension Arrays of Waveguides

Quantum walks (QWs) have emerged from fundamental research to be one of key processes in quantum information technology including quantum computing and quantum communication. In this paper, we present results of our numerical investigation of quantum walks (QWs) in different types of 2D arrays of waveguides. We show (i) the localized QWs in quasiperiodic arrays based on Fibonacci sequences are highly controllable due to the deterministically disordered nature of quasiperiodic photonic lattices, (ii) 2D arrays of waveguides can also be used as platforms to realize important effects for special applications such as exponential speedup in quantum search and quantum topology photonics and finally, (iii) results of multiple photons QWs in 2D programable directional couplers can be useful for designing quantum photonics gates.